Preheat the oven to 350 degrees F (175 degrees C). Line 2 baking sheets with parchment paper.

Mix carrots, oats, and apple together in a large bowl. Whisk peanut butter and eggs until thoroughly combined in a second bowl. Pour into the oat mixture and stir until thoroughly combined.

Drop 1 1/2 tablespoonfuls of batter onto the prepared baking sheets. Flatten each treat with your hands until they are 1/2-inch thick.

Bake in the preheated oven until treats are firm to the touch and begin to brown on the bottom, 15 to 20 minutes. Allow to cool a few minutes on the baking sheets before removing to a wire rack to cool completely.